# Unweighted Index Numbers

There are two methods of constructing unweighted index numbers. (1) Simple Aggregative Method (2) Simple Average of Relative Method

Simple Aggregative Method:

In this method, the total of the prices of commodities in a given (current) years is divided by the total of the prices of commodities in a base year and expressed as percentage.

Simple Average of Relatives Method:

In this method, we compute price relative or link relatives of the given commodities and then use one of the averages such as arithmetic mean, geometric mean, median etc. If we use arithmetic mean as average, then

The simple average of relative method is very simple and easy to apply is superior to simple aggregative method. This method has only disadvantage that it gives equal weight to all items.

Example:

The following are the prices of four different commodities for $1990$ and$1991$. Compute a price index by (1) Simple aggregative method and (2) Average of price relative method by using both arithmetic mean and geometric mean, taking$1990$ as base.

 Commodity Cotton Wheat Rice Gram Price in$1990$ $909$ $288$ $767$ $659$ Price in $1991$ $874$ $305$ $910$ $573$

Solution:
The necessary calculations are given below:

 Commodity Price in$1990$ ${P_o}$ Price in $1991$ ${P_n}$ Price Relative $P = \frac{{{P_n}}}{{{P_o}}} \times 100$ $\log P$ Cotton $909$ $874$ $\frac{{874}}{{909}} \times 100 = 69.15$ $1.9829$ Wheat $288$ $305$ $\frac{{305}}{{288}} \times 100 = 105.90$ $2.0249$ Rice $767$ $910$ $\frac{{910}}{{767}} \times 100 = 118.64$ $2.0742$ Gram $659$ $573$ $\frac{{573}}{{659}} \times 100 = 86.95$ $1.9393$ Total $\sum {P_o} = 2623$ $\sum {P_n} = 2662$ $\sum P = 407.64$ $\begin{gathered} \sum \log P \\ = 8.0213\\ \end{gathered}$

(1) Simple Aggregative Method:

(2) Average of Price Relative Method (using arithmetic mean):

Average of Price Relative Method (using geometric mean)